57. Consider the additive random-effects model X jk = J.L + Ai + Bj + U;jk (i=l,. ..,a; j=l, .. . ,b; k=l, . . . ,n), where the A's, B's, and U's are independent normal with zero means and variances a], aJ, and a2 respectively. Determine (i) the joint density of the X's, (ii) the UMP unbiased test of H : aVa2 S 6.